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Sample Paper – 2013
Class – IX
Subject –MATHEMATICS

Practice all these questions. These questions will certainly strengthen your basics for A-form.

  1. Cube A has side 2 cm. Cube B has side 4 cm. What is ?
  2. The equation has a solution x =-2. What is a?
  3. The mean weight of a group of 11 men is 70kg. What is the mean weight of the remaining group when a man of weight 90 kg leaves?
  4. The circumference of a circle is 16cm. Find its area.
  5. Make x as the subject: .
  6. A car travels for 20 minutes at 45 km/h and then for 40 minutes at 60 km/h. Find average speed for the whole journey.
  7. Find the value of each interior angle of a regular polygon of 18 sides.
  8. Adjacent angles in a parallelogram are . Find the value of each angle of the parallelogram.
  9. A rectangle 8 cm by 6 cm is inscribed inside a circle. What is the area of the circle?
  10. When the sides of a square are increased by 10%. By what percentage its area is increased?
  11. Solve :
  12. Given that find the value of .
  13. What fraction of the area of a rectangle is the area of the triangle?
  1. On a map a distance of 36 km is represented by a line of 1.8 cm. What is the scale of the map?
  2. Given that then find
  3. A triangle has sides of length 5 cm, 5cm and 6 cm. What is its area in Cm2?
  4. A glass paperweight consists of a cone mounted on a hemisphere. The common radius® is 3 cm; the height of the one c(h) is 4 cm. (i) Calculate the volume and surface area of the paper weight.

(ii) 1 cm3of the glass of which the paperweight is made weighs 2.85g. Calculate the mass of the paperweight.

  1. In an experiment, 50 people were asked to guess the weight of a bunch of daffodils in grams. The guesses were as follows:

47, 39, 21, 30, 42, 35, 44, 36, 19, 52, 23 , 32, 66, 29, 5, 40, 33, 11, 44, 22, 27, 58, 38, 37, 48, 63, 23, 40, 53, 24, 47, 22, 44, 33, 13, 59, 33, 49, 57, 30, 17,45, 38, 33, 25, 40, 51, 56, 28, 64.

Construct a frequency table using intervals 0-9,10-19,20-29, etc.

Draw a histogram and frequency polygon.

Find the mean weight.

  1. In a survey of the number of occupants in a number of cars, the following data resulted.

No. of occupants / 1 / 2 / 3 / 4
No. of cars / 7 / 11 / 7 / x

(a)If the mean number of occupants is , find x.

(b)If the mode is 2, find the largest possible value of x.

(c)If the median is 2, find the largest possible value of x.

  1. For the set of numbers below, find the mean and median:

1,3,3,3,4,6,99.

Which average best describes the set of numbers?

  1. In a form of 30 girls, 18 play netball and 14 play hockey, whilst 5 play neither. Find the numbers who play both netball and hockey.
  1. A ladder of length 6 m leans against a vertical wall so that the base of the ladder is 2 m from the wall. Calculate the angle between the ladder and the wall.
  2. If , find .
  3. Find the value of x:
  1. (a)Construct a triangle ABC in which AB=8cm, AC=6cm and BC=9cm.

(b)Construct the bisector of .

(c) Construct the line through C perpendicular to CA and mark the point X where this line meets

the bisector of BAC.

(d)Measure the lengths CX and AX.

  1. Three positive integers are (x-1), x and (x+1). When they are multiplied together the answer is 40 times their sum. Find the integers.
  2. A man goes out at 16:42 and arrives at a post box, 6 km away, at 17:30. He walked part of the way at 5 km/hr and then, realizing the time, he ran the rest of the way at 10km/hr. How far did he have to run?
  3. The ratio of men: women: children living in a town are 6:7:3. There are 42000 women.

(a)(i) How many children live in the town? (ii) How many people altogether live in the town.

(b)The 42000 women is an increase of 20% on the number of women ten years ago. Calculate how many women lived in the town ten years ago?

(c)Twelve thousand of the children attend school and 48% of them are boys.

(i)Calculate the number of boys and the number of girls at school.

(ii)The average age of the 12000 children is exactly 10.54 years. The average age of the boys is exactly 10.35 years. Calculate the average age of the girls, correct to two decimal places.

  1. A map is drawn to a scale of 1:20000. Find the actual distance between two points, which appear 5 cm apart on the map. Also, the area, in sq.km of a lake which has an area of 20cm2 on the map.
  2. The minute hand of a clock has a length of l from its point of rotation to the point at the end of the arrow. What is the total distance travelled by the point at the end of the arrow in m minutes.
  3. How many integers between 100 and 999 inclusive have a units digit of 7?
  4. At a certain hour, a lamppost that stands 108 inches tall casts a shadow 27 inches long. Sue is f inches tall. In terms of f, how many inches long is her shadow at the same hour?
  5. If find the value of:
  6. State and prove Pythagoras theorem.
  7. At a clothing store, the price of a cashmere sweater is three times the price of a cotton sweater. If the store sold 25 cashmere sweaters for a total of $ 1500 and the combined sales of cashmere and cotton sweaters totaled $1800, how many cotton sweaters were sold?
  8. In the rectangle below if x = 40, then find y + z.
  1. The perimeter of this rectangular field is 220 m. One side is x m as shown.

(a)Express the width (W) in terms of x.

(b)Write an expression, in terms of x only, for the area of the field.

(c)If the length (x) is 70 m, find the area.

  1. Angela needs $4000 to pay for a car. She was given two options by the car seller.

Option A: Outright Loan

A loan of $4000 at a rate of 12% per annum compounded monthly.

(a)Find (i)the cost of this loan for one year;

(ii)the equivalent annual simple interest rate.

Option B: Friendly Credit Terms

A 25% deposit, followed by 12 equal monthly payments of $287.50.

(b)(i)How much is to be paid as a deposit under this option?

(ii)Find the cost of the loan under Friendly Credit Terms.

(c)Give a reason why Angela might choose

(i)Option A (ii)Option B

To help Angela, her employer agrees to give her an interest free loan of $4000 to buy the car. The employer is to recover the money by making the following deductions from Angela’s salary: $x in the first month,

$y every subsequent month.

The total deductions after 20 months is $1540 and after 30 months it is $2140.

(d)Find x and y.

(e)How many months will it take for Angela to completely pay off the $4000 loan?

  1. Keisha had 10 000 USD to invest. She invested m USD at the Midland Bank, which gave her 8% annual interest. She invested f USD at the First National Bank, which gave 6% annual interest. She received a total of 640 USD in interest at the end of the year.

(a)Write two equations that represent this information.

(b)Find the amount of money Keisha invested at each bank.

  1. The table shows the number of children in 50 families.

Number of
children / Frequency / Cumulative
frequency
1 / 3 / 3
2 / m / 22
3 / 12 / 34
4 / p / q
5 / 5 / 48
6 / 2 / 50
T

(a)Write down the value of T.

(b)Find the values of m, p and q.

  1. The bar chart below shows the number of people in a selection of families.

(a)How many families are represented?

(b)Write down the mode of the distribution.

(c)Find, correct to the nearest whole number, the mean number of people in a family.

  1. The cost of living in a country is increasing by 3% each year.

(a) what is the growth factor ?

(b) What will be the total percentage increase after (i) 2 years, (ii) 18 months ?

(c) write an expression for the percentage increase after n years ?

  1. Given that log 2 (x – 5 y + 4 ) = 0 and log 2 ( x + 1 ) – 1 = 2 log 2 y, find x and y.
  2. Solve the following simultaneous equations:

2 log2 x = y

log2 2x = y + 4

  1. Given XY = 2 cm, BC = 3 cm and area of XYCB = 10 cm2, find the area of triangle

AXY.

  1. The heights of 200 students are recorded in the following table.

Height (h) in cm / Frequency
140 ≤ h < 150 / 2
150 ≤ h < 160 / 28
160 ≤ h < 170 / 63
170 ≤ h < 180 / 74
180 ≤ h < 190 / 20
190 ≤ h < 200 / 11
200 ≤ h < 210 / 2

(a)Write down the modal group.

(b)Calculate the mean of the heights.

  1. 300 apples are distributed equally among certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.
  2. The perpendicular AD on the base BC of triangle ABC intersect BC in D, such that BD = 3 CD. Prove that .
  3. Evaluate:
  4. Prove:
  5. Evaluate sin700 + tan10 tan40 tan50 tan80

cos 20 2 cos 430 cosec 470

  1. In an equilateral triangle ABC, D is a point on side BC such that BD = BC.

Prove that 9AD2 = 7AB2.

  1. A farmer connects a pipe of internal diameter 20cm from a canal into a

cylindrical tank in her field, which is 10m in diameter and 2m deep. if water

flows through the pipe at the rate of 3km/hr, in how much time will the tank to

be filled?

  1. The mean of the following data is 28.5.Find the missing frequencies x and

y, if the total frequency is 60

Class interval / Frequency
0-10 / 5
10-20 / X
20-30 / 20
30-40 / 15
40-50 / Y
50-60 / 5

(a)Solve: (x+2) (x-5) (x-6)(x+1) =144.

(b) Solve: = x+2

Mathematics can be learnt only by continuous practice.

“Efficiency is the capacity to bring proficiency into expression”.

“Wisdom is the assimilated knowledge in us, gained from an intelligent estimation and close study of our own direct and indirect experience in the world.”

Paper Submitted By:

NameChandan Singh Ghughtyal

Phone No.7579016459


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